ADK Forever Wild: So how do they measure mountains?

Saturday, November 15, 2014

So how do they measure mountains?

The system Colvin used when measuring Seward is still used today in fancy watches and in most GPS units equipped with barometric altimeters. Instead of a big glass tube filled with mercury they use electronic sensors smaller than a fingernail which measure both pressure and temperature and use the two values and a bunch of equations to calculate an elevation. This is fairly accurate (my GPS reports values down to foot, and is probably accurate to around 10 ft or so depending on how well it was calibrated).

One of the current mapping systems uses lasers to measure distance (instead of the radio waves used by radar) and is known more broadly as LiDAR. They time how long it takes a laser pulse to reach an object and return to the source. If you fly this system over an area of land either in a satellite or an airplane, and you pick the right wavelength of light so some of it will reflect back, you can get a very detailed profile. Your accuracy is good since satellite orbits are very well defined or you could correct for errors with the airplane's positioning system. I'm fairly sure that LiDAR is the source of the data that Google has used to create their fantastic terrain maps in their mapping programs.

Surveyors also use laser based systems to measure distances. In fact, it wouldn't be that hard for two people to stand on two different peaks in the Adirondacks, align a laser and a mirror, and let the system very accurately measure the difference in altitude between the two peaks with simple trigonometry.

GPS can also be used to measure heights and works on a similar principle. The key is having very accurate clocks in both the satellite and the device to calculate the travel time for the signal: the more accurate (and expensive) the clock, the better the data. If you leave the GPS system up on top of the mountain long enough for the satellites to make several orbits in different environmental conditions it can measure the height with an acceptable uncertainty.

But when we say something is 5,000 ft above sea level, what are we really saying? It's easy to measure the height of a building because you have two fixed reference points: the ground and the top of the building which (hopefully) doesn't move around that much. But on top of a mountain, which spot is the peak? When you're measuring growth of mountains, the thickness of a piece of lichen matters. But that's not even the strangest thing: when we say "sea level" what are we talking about? High tide, low tide, somewhere in between? The Earth isn't even a perfect sphere, so, with everything else held constant, one person's high tide could actually be higher than someone else's. The article were I found this intriguing idea suggests that there are formulas for calculating a standard "sea level," but it's still amusing that we have to define as concrete an idea as elevation in terms of unpredictable things like "sea level."